When you pass another user in StreetPass mode, your Mii characters will automatically hop across to the other player's console, appearing in the StreetPass Mii Plaza. In Iwata's words:

In short, this software enables you to enjoy collecting various Mii characters by passing other Nintendo 3DS users. We have added two small games you can easily play. One is the game called "StreetPass Quest."

While Iwata didn't give any further information about the game, he did reveal it's become quite the social success inside Nintendo, with many developers carrying prototype consoles just to test out this feature.

Many of them even go back and forth in the building, without any business purpose, to collect as many Mii characters as possible or secretly check their Nintendo 3DS during meetings. In fact, I am also one of them.